Mechanics | Relativity Answers

Two crates, A and B, sit at rest side by side on a frictionless horizontal surface. The crates have masses mA and mB. A horizontal force is applied to crate A and the two crates move off to the right. (a) Draw clearly labelled free-body diagrams for crate A and for crate B. Indicate which pairs of forces, if any, are third-law action-reaction pairs. (b) If the magnitude of force is less than the total weight of the two crates, will it cause the crates to move? Explain.

A particle moving at 30 m/s West has a momentum of 1598 kg.m/s West, calculate the mass of the particle.

a car moving at a speed of 25 m/s in the postive direction decelerates to a stop in 5.0 s. The average acceleration of the car over the 5.0s is

The position of a particle moving along the x-axis is determined by the

equation

d^2x/dt^2+8x=20cos2t

. If the particle starts from rest at x = 0,



determine

(i) The position x as a function of time

(ii) The amplitude, period and frequency of oscillation after a long time has elapsed

1. An athlete throws a ball of mass m directly upward, and it feels no appreciable air resistance. Draw a free-body diagram of this ball while it is free of the athlete's hand and (a) moving upward; (b) at its highest point; moving downward. (d) Repeat parts a, b, and c if the athlete throws the ball at a 60-degree angle above the horizontal instead of directly upwards.

1. A ball is hanging from a long string that is tied to the ceiling of a train car travelling castward on horizontal tracks. An observer inside the train car sees the ball hang motionless. Draw a clearly labelled free-body diagram for the ball if (a) the train has a uniform velocity, and (b) the train is speed up uniformly. Is the net force on the ball zero in either case? Explain.

1. If the action is a bowstring acting on an arrow, what is the reaction force?
2. A person stands still. The upward support of the floor is a reaction force. What is the action force?

1. We know that Earth pulls on the moon. Does the moon pull on Earth? If so, which pull is stronger?

1. You are trying to move a 500-N crate across a level floor. To start the crate moving, you have to pull with a 230-N horizontal force. Once the crate "breaks loose" and starts to move, you can keep it moving at constant velocity with only 200-N.
a. Draw a free-body diagram for crate just before it starts to move.
b. What forces are acting on the crate just before it starts to move?

3. A subway train is at rest at station A
and must depart for station B. They are
1000 m apart from each other, and the
train can accelerate at no greater than
2 m/s2
(or less than −2 m/s2
). The

train must begin at rest (0 m/s) at sta-
tion A and end at rest at station B.

a. Design a subway trip consisting of three phases: 1) the train speeds up from rest, 2) the
train travels at a constant velocity, and 3) the train slows down to a stop. Your trip must
be exactly 1000 m in total displacement, and the magnitude of the train’s acceleration
cannot exceed 2 m/s2

(but you may use a smaller acceleration if you wish). You may
draw a graph, a diagram of the train itself, or simply provide calculations. It may help
to imagine your own experiences on a subway trip.

b. For each of the three phases of the train’s motion, how much time does each phase take
under your design? What is the maximum velocity of your train?