A sled is being held at rest on a slope that makes an angle with the horizontal. After the sled is released, it slides a distance d₁ down the slope and then covers the distance d₂ along the horizontal terrain before stopping. Find the coefficient of kinetic friction μ between the sled and the ground, assuming that it is constant throughout the trip. Solve Part B Find the coefficient of kinetic friction μk. Express your answer in terms of some or all of the variables d1, d2, and 0.

A 0.400-kg pendulum bob passes through the lowest part of its path at a speed of 3.00 m/s. (a) What is the tension in the pendulum cable at this point if the pendulum is 80.0 cm long? (b) When the pendulum reaches its highest point, what angle does the cable make with the vertical? (c) What is the tension in the pendulum cable when the pendulum reaches its highest point?

If the vector components of the position of a particle moving in the xy plane as a function of time are x(t)=(2.5ms2)t2i and y(t)=(5.0ms3)t3j, when is the angle between the net force on the particle and the x axis equal to 45?

Check Your Understanding A block of mass 1.0 kg rests on a horizontal surface. The frictional coefficients for the block and surface are s=0.50and k=0.40 . (a) What is the minimum horizontal force required to move the block? (b) What is the block’s acceleration when this force is applied?

Suppose the mass of a fully loaded module in which astronauts take off from the Moon is 1.00104kg . The thrust of its engines is 3.00104N . (a) Calculate the module’s magnitude of acceleration in a vertical takeoff from the Moon. (b) Could it lift off from Earth? If not, why not? If it could, calculate the magnitude of its acceleration.

If a single constant force acts on an object that moves on a straight line, the objects velocity is a linear function of time. The equation v = vi + at gives its velocity v as a function of time, where a is its constant acceleration. What if velocity is instead a linear function of position? Assume that as a particular object moves through a resistive medium, its speed decreases as described by the equation v = vi kx, where k is a constant coefficient and x is the position of the object. Find the law describing the total force acting on this object.

An object of mass m is sliding with speed vi at some instant across a level tabletop, with which its coefficient of kinetic friction is . It then moves through a distance d and comes to rest. Which of the following equations for the speed vi is reasonable? (a) vi=2mgd (b) vi=2mgd (c) vi=2gd (d) vi=2gd (e) vi=2d

A particle is projected with an initial velocity 0 up a slope that makes an angle with the horizontal. Assume frictionless motion and find the time required for the particle to return to its starting position. Find the time for 0 = 2.4 m/s and = 26.

Consider a projectile fired vertically in a constant gravitauonal field. For the same initial velocities, compare the times required the projectile to reach its maximum height (a) for zero resisting force, (b) for a resisting force proportional to the instantaneous velocity of the projectile.

A particle of mass m has speed υ = α/x, where x is its displacement. Find the force F(x) responsible.