Concept explainers
(a)
The initial speed of the block.
(a)
Answer to Problem 83P
The initial speed of the block is
Explanation of Solution
Figure 1 represents that a block slides up a frictionless inclined plane.
From the above figure
Figure 2 represent the free body diagram of the block ignoring friction.
Write the expression for net force acting on the block in the
The above equation can be written as
Write the expression for net force acting on the block in the
The above equation can be written as
Write the kinematic equation.
Here,
Since the final velocity of the block is zero and the initial position of the block is zero, the above equation is written as
Use equation (I) and (II) in the above equation.
Conclusion:
Substitute
Therefore, the initial speed of the block is
(b)
The initial speed required for the block to reach the maximum height.
(b)
Answer to Problem 83P
The initial speed required for the block to reach the maximum height is
Explanation of Solution
Figure 3 represent the free body diagram of the block by considering friction.
Write the expression for net force acting on the block in the
The above equation can be written as
Write the expression for frictional force.
Here,
Use the above equation in equation (IV).
Write the kinematic equation.
Here,
Since the final velocity of the block is zero and the initial position of the block is zero, the above equation is written as
Use
Conclusion:
Substitute
Substitute
Therefore, the initial speed required for the block to reach the maximum height is
Want to see more full solutions like this?
Chapter 4 Solutions
College Physics, Volume 1
- A spring cannon fires a marble at 45 ° up from horizontal going 2.0 m/s and starting 1.0 m above the floor. Assuming that the marble does not hit anything on its way to the floor, and ignoring air drag, which of the following is true of the | vx | (magnitude of the horizontal velocity component) and | vy | (magnitude of the vertical velocity component) of the marble as it goes up (but has not yet reached its maximum height)? a) | vx | Decreasing & | vy | Decreasing b) | vx | Constant & | vy | Decreasing c) | vx | Decreasing & | vy | Constant d) | vx | Constant & | vy | Constant e) None of these.arrow_forwardIn Figure P4.53, the incline has mass M and is fastened to the stationary horizontal tabletop. The block of mass m is placed near the bottom of the incline and is released with a quick push that sets it sliding upward. The block stops near the top of the incline as shown in the figure and then slides down again, always without friction. Find the force that the tabletop exerts on the incline throughout this motion in terms of m, M, g, and .arrow_forwardIn a shuffleboard game, the puck slides a total of 12 m on a horizontal surface before coming to rest. If the coefficient of kinetic friction between the puck and board is 0.10, what was the initial speed of the puck? 48.5 m/s 4.8 m/s 4.3 m/s 3.8 m/sarrow_forward
- A 4.4 kg block located on a horizontal floor is pulled by a cord that exerts a force F = 10 N at an angle theta = 35 degrees above the horizontal, as shown. The floor has a coefficient of kinetic friction µk = 0.1. What is the magnitude of the acceleration [m/s2] of the block? What is the horizontal speed [m/s] of the block 4.4 seconds after it starts moving?arrow_forwardA trained sea lion slides from rest with constant acceleration down a 3.0-m-long ramp into a pool of water. If the ramp isinclined at an angle of u = 23° above the horizontal and the coefficient of kinetic friction between the sea lion and theramp is 0.26, how much time does it take for the sea lion to make a splash in the pool?arrow_forwardA skier with a mass of 60 kg is sliding down a snowy slope, the slope with an angle of 30 degrees above the horizontal as shown in the figure. Find the acceleration for the skier if friction is known to be 45.0 N. Assuming no air resistance and g=10m/s^2. a) 10 m/s^2 b) 0.75 m/s^2 c) 4.25 m/s^2 d) 1.33 m/s^2arrow_forward
- You are a member of an alpine rescue team and must get a box of supplies, with mass 2.80 kg , up an incline of constant slope angle 30.0 degrees so that it reaches a stranded skier who is a vertical distance 3.10 m above the bottom of the incline. There is some friction present; the kinetic coefficient of friction is 6.00×10^−2. Since you can't walk up the incline, you give the box a push that gives it an initial velocity; then the box slides up the incline, slowing down under the forces of friction and gravity. Take acceleration due to gravity to be 9.81 m/s2. Use the work-energy theorem to calculate the minimum speed v that you must give the box at the bottom of the incline so that it will reach the skier.arrow_forwardA skier of mass 65.0 kg is pulled up a snow-covered slope at constant speed by a towrope that is parallel to the ground. The ground slopes upward at a constant angle of26.0 degree above the horizontal, and you can ignore friction. Draw a clearly labelled FBD forthe skier.arrow_forwardA man is driving his SUV with speed 51.0 mi/h on a horizontal stretch of road. (a) When the road is wet, the coefficient of static friction between the road and the tires is 0.104. Find the minimum stopping distance (in m). m (b) When the road is dry, μs = 0.596. Find the minimum stopping distance (in m). marrow_forward
- You are standing at the top of a cliff that has a stairstep configuration. There is a vertical drop of 6 m at your feet, then a horizontal shelf of 5 m , then another drop of 4 m to the bottom of the canyon, which has a horizontal floor. You kick a 0.44 kg rock, giving it an initial horizontal velocity that barely clears the shelf below What initial horizontal velocity v will be required to barely clear the edge of the shelf below you? The acceleration of gravity is 9.8 m/s^2 . Consider air friction to be negligible. Answer in units of m/s. How far from the bottom of the second cliff will the projectile land? Answer in units of m.arrow_forwardYou are a member of an alpine rescue team and must get a box of supplies, with mass 2.30 kg , up an incline of constant slope angle 30.0 ∘ so that it reaches a stranded skier who is a vertical distance 2.50 m above the bottom of the incline. There is some friction present; the kinetic coefficient of friction is 6.00×10−2. Since you can't walk up the incline, you give the box a push that gives it an initial velocity; then the box slides up the incline, slowing down under the forces of friction and gravity. Take acceleration due to gravity to be 9.81 m/s2. Use the work-energy theorem to calculate the minimum speed v that you must give the box at the bottom of the incline so that it will reach the skier. Express your answer numerically, in meters per second.arrow_forwardYou are given the job of moving a refrigerator with a mass of 1.8 x 102 kg across a horizontal floor. The coefficient of static friction between the refrigerator and the floor is 0.45. Calculate the magnitude of the minimum force that is required just to set the refrigerator into motion.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-HillPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning