Homework 4

Problem 3:A man is pushing a lawnmower, and he exerts a force that has a horizontal component ofF=F=33N. A horizontal frictional force has a magnitudef=f=11N, which opposes the horizontal component of the pushing force. The mass of the lawnmower ism=m=39kg.

a)Write an expression for the magnitude of the acceleration of the lawnmower.

a =

b)If the lawnmower starts from rest, then what is its speed, in meters per second, at time t=2.00s?

v = m/s

c)Suppose the man stops pushing on the lawnmower at t=2.00s. Assuming the frictional force is constant, what distance, d, in meters, does the lawnmower roll before coming to rest?

d = m

Problem 4:A block with massm₁=8.1kg rests on the surface of a horizontal table which has a coefficient of kinetic friction of_k=0.75. A second block with a massm₂=12kg is connected to the first by an ideal string passing over an ideal pulley such that the second block is suspended vertically. The second block is released from rest, and motion occurs.

a)Using the variable T to represent tension, write an expression for the sum of the forces in the y-direction, F_y, for block 2.

F_y =

c)Block 1 accelerates along the tabletop, in the horizontal direction, while block 2 moves vertically. With the coordinate system provided in the drawing, we may write a1=a1i^a1=a1i^ and a2=a2y^a2=a2y^. Write an expression that relates the vertical component of the acceleration of block 2 to the horizontal component of the acceleration of block 1.

a₂ =