A hot-air balloon of mass 220 kg is descending vertically with downward acceleration of magnitude 1.4 m/s?. How much mass (ballast) must be thrown out to give the balloon an upward acceleration of magnitude 1.4 m/s² (same magnitude but opposite direction)? Assume that the upward force from the air (the lift) does not change because of the decrease in mass. Number i Units

An object of mass 13.0-kg subjected to a non-zero net force moves with an acceleration of (8.00î – 5.0oĵ) m/s². (a) Determine the magnitude and direction of the net force acting on it. magnitude direction ° counterclockwise from the +x axis (b) What acceleration would a 32.5-kg object have if the same net force is applied to it? Express your answer in vector form. a = m/s?

Write an expression for the component of net force, Fnet,x, in the x direction, in terms of the variables given in the problem statement. Fnet,x=

Please answer all the parts

A cart of mass 8.0kg was moved by applying two constant forces. Force 1 is 28.0N at 42.0 degrees, and Force 2 is 13.0N at 110 degrees. Initially, the cart has a velocity of (3.50i + 2.20j)m/s. a. Express the two forces in unit-vector notation.b. Find the total force exerted on the cart.c. Find the angle at which the total force is applied.d. What is the acceleration of the cart?e. What is the cart's velocity after 5.0s?f. What is the position of the cart after 5.0s?g. What is the angle of the position after 5.0s?h. What is the total work done by the two applied forces?

A 1.9 kg otter starts from rest at the top of a muddy incline 84.1 cm long and slides down to the bottom in 0.60 s. What net external force acts on the otter along the incline? Answer in units of N.

A particle, which remains at rest, is acted on by three forces F, G and H. The force F has magnitude 55 N and is directed to the left and up making an angle of 45 degrees with the vertical The force G is directed vertically down and H is directed to the right and up making an angle of 60 degrees with the vertical. Find the magnitude of the vectors G and H, giving your answers to one decimal place. The magnitude of G is N (to 1 d.p.) The magnitude of H is N (to 1 d.p.)

While moving in, a new homeowner is pushing a box across the floor at a constant velocity. The coefficient of kinetic friction between the box and the floor is 0.393. The pushing force is directed downward at an angle below the horizontal. When is greater than a certain value, it is not possible to move the box, no matter how large the pushing force is. Find that value of 0. Number i Units

a)A block of mass m = 170 kg rests against a spring with a spring constant of k = 680 N/m on an inclined plane which makes an angle of θ degrees with the horizontal. Assume the spring has been compressed a distance d from its neutral position. b)Enter an expression for the normal force, FN, that the plane exerts on the block (in the y-direction) in terms of defined quantities and g.  c)Denoting the coefficient of static friction by μs, write an expression for the sum of the forces in the x-direction just before the block begins to slide up the inclined plane. Use defined quantities and g in your expression  d) Assuming the plane is frictionless, what will the angle of the plane be, in degrees, if the spring is compressed by gravity a distance 0.1 m?  e) If the velocity at the bottom is the same as the velocity at the top from part (a), what is the child's apparent weight, in newtons, at the very bottom of the path?

Many physical properties, such as force and mass, cannot be measured directly. Rather, some other physical property is measured and the desired physical property is computed from the results. For example, a bathroom scale does not actually measure mass or "weight," but rather the compression distance of a spring. The numerical values on the scale are calibrated from the compression distance using basic physics principles such as Newton's second law. Coefficients of friction cannot be measured directly. In this problem, we are going to learn how we can indirectly measure the coefficient of kinetic friction between two surfaces by directly measuring the expansion of a spring. Consider a 5.45 kg5.45 kg block that is dragged by a spring on a (relatively) frictionless horizontal surface at constant velocity. Suppose the block reaches a rough patch and the spring stretches by 5.25 cm5.25 cm. Compute the coefficient of kinetic friction ?μ between the block and the rough patch if the spring…