Problems

Chapter 4,5

Problem 1 A ball from a tower of height 30 m is projected down at an angle of 30° from the horizontal with a speed of 10 m/s. How long does it take the ball to

reach the ground. (Consider g = 10 m/s2 ):

smvvy /530sin10sin00

st

tt

tt

gttvy y

3

06

102

1530

2

1

2

2

20

By using the equation

Neglecting negative value of time, t = -2 s

Solution:

Problem 2

On a hot summer day a young girl swings on a rope above the local swimming hole. When she lets go of the rope her initial velocity is 2.25 m/s at an angle of 35.0° above the horizontal. If she is in flight for 1.60 s, how high above the water was she when she let go of the rope?

v0 = 2.25 m/s

v0x = v0 cos(35) = 1.8 m/s

v0y = v0 sin(35) = 1.3 m/s

Solution:

y = y0 +v0y t – (1/2) g t2

y-y0 = - 10.5 m

y =0

y0 = +10.5 m

By using

Problem 3A projectile is launched horizontally with an initial speed v0 from a height y0. Neglect aerodynamic friction.

v0 = 3.5 m/sy0 = 4.0 m

)1 (What is the time t for the projectile to reach the ground ?

v0

x

y

y0

0

0.42

1

0

0

200

y

y

v

my

gttvyy

90.0

816.0)81.9/()0.4(2

2

10.40

0

2

2

t

t

gt

y

Solution:

(a)2 (What is the horizontal component of the projectile’s velocity when it hits the ground?

smv

a

smv

tavv

x

x

x

xxx

/5.3

0

/5.30

0

smv

smssmgtvv

smv

vvv

yy

x

yx

/53.9

/86.8)90.0)(/81.9(

/5.32

0

22

)3 (What is the speed of the projectile when it hits the ground?

Problem 4

Suppose we have a situation as we did in a lab experiment, in which a hanging mass and cart are connected by a string over a pulley.

The hanging mass is 0.20 kg, but we don't know the mass of the cart. After the cart is released and the objects are moving, the tension in the string is found to be 1.80 N.

)A (Find the acceleration of the hanging mass. First, draw a free-body diagram

)B (Find the mass of the cart, assuming that there is no friction .

)C (find the mass of the cart assuming that there is a 0.50 N frictional force acting on the cart.

Problem 5Find the tensions in each string in the figure at right. They are attached to a wall and ceiling, as shown, and are holding up a mass of 10 kg

Knowing T1, we can find T2:

Solution:

Problem 6We show below two blocks connected by a light string and pulled by a string in front. The “front” block has a mass of 5.0 kg and the other block’s mass is 2.0 kg. The large block slides on frictionless surface. The back, smaller block has a rough bottom surface which creates a frictional force of 6.0 N. The tension T1 in the front string is 20.0 N. Determine the tension T2 in the middle string

Solution:

Problem 7A 20-kg box is sitting on the floor and someone is pulling on it with a rope. The tension in the rope is 60 N at an angle 60◦ above the horizontal. However, the box does not move. It just sits there, held by static friction.

)a (Draw a free-body diagram of the box.

)b (Find the normal force that the floor exerts on the box.

Problem 8 Two forces F1 and F2 act on a 5.00-kg object. If F1 = 20.0 N and F2 = 15.0 N, find the accelerations in (a) and (b) of Figure

Problem 9 A 3.00-kg object is moving in a plane, with its x and y coordinates given by x = 5t2 + 1 and y =3t 3 + 2, where x and y are in meters and t is in seconds. Find the magnitude of the net force acting on this object at t = 2.00 s

Quiz

)1 (A projectile is fired in such a way that its horizontal range is equal to three times its maximum height. What is the angle

of projection?

)2 (An inclined plane makes an angle 20◦ with the horizontal. A 0.20-kg bar of soap slides down the incline, and experiences a frictional force of 0.20 N. (A) Draw a free-body diagram of the bar of soap. (B) Find the net force on the bar of soap. (C) Calculate the rate of acceleration of the bar of soap