A box of mass m is on a horizontal surface. It is connected by a string, which p
ID: 1960841 • Letter: A
Question
A box of mass m is on a horizontal surface. It is
connected by a string, which passes over a pulley, to a
cart of mass m. The cart is on a ramp, which takes the
form of a 3-4-5 triangle. We can neglect friction
between the cart and the ramp, as well as in the pulley,
but there is friction between the box and the horizontal
surface. Initially, the system is at rest, and the force of staticfriction keeping the box at rest is at its maximum possible value.
1) The coefficient of kinetic friction between the box and the surface is only 0.40, so,
when the box is given a small push to the right, the system then starts to move with a constant
acceleration to the right. Neglecting the small push, which just served to start the motion,
calculate the value of this acceleration. SHOW WORK!
Use the free-body diagram of the box to determine the magnitude of the force of
tension, while the system has its constant acceleration. Show work particularly clearly here!
Use the free-body diagram of the cart to determine the magnitude of the force of
tension, while the system has its constant acceleration. Show work particularly clearly here!
Explanation / Answer
WRITING EQNS ON HORIZONTAL SURFACE BLOCK
T-*m*g=m*a
T-.40*m*10=m*a ---1
writing eqns on cart
m*g*sin-T=m*a ( is angle between 5m and 4m leg)
sin=3/5 ----------2
adding eqns 1 and 2
m*6-4*m=2*m*a
a=1m/s^2
T=m*a+4*m
=5*m
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