Question

A small mass m slides with negligible friction down an incline at an angle of 25.76° with respect to the horizontal. It then drops down to a horizontal surface andbounces elastically back up as shown.

The picture is to scale. It shows the position of the mass at equal time intervals starting from rest at V. The height of the mass at P is the same as at U.

Answer Choices: G-Greater than, L-Less Than, E-Equal to

(a) The speed change between V and X is____ between X and T.

(b) The velocity of m at U is ____ that at P.

(c) The size of the total force on m at R is____ at S.

(d) The speed of m at S is_____ that at Q.

(e) The size of the total force on m at Q is_____ at X.

(f) The mechanical energy of m at P is_____ that at Q.

Answer 1

a. The particle is under a constant acceleration so we can apply the kinematic formula Δv = aΔt. Clearly the time it takes to travel from V to X is grater than that from X to T (the particle is simply moving faster from X to T). Thus this is a is > than

b. The energy of the particle is constant. If U and P are at the same height as they appear to be, their potential energy is the same. Thus, their kinetic energy is the same. Hence, they have equal velocities. If you want to quibble about sign you can but since their is no defined axis it just makes more sense to say that their speeds are equal.

c.If you think about force as F = Δp/Δt you can see that at R the change in momentum is very large while at S it is significantly smaller. Thus R > S.

d. At Q it only has the horizontal component whereas at S it has both the same horizontal component and a vertical component. Hence S > Q.

e.The force on X is only the component of gravity down the slope: the rest is cancelled by the normal force. At Q it is the entire force of gravity. Hence Q>X

f. There is no friction in the system. Without nonconservative forces, energy is constant. Hence P = Q.

I hope this is helpful to you.