Question

A block of ice

(m = 14.0 kg)

with an attached rope is at rest on a frictionless surface. You pull the block with a force of 91.0 N for 1.41 s at an angle of 18.0°. (The angle is above the horizontal.)

(a) Determine the magnitude of each force acting on the block of ice while you are pulling.

Fpull	=	N
Fg	=	N
FN	=	N

(b) With what speed is the ice moving after you are finished pulling?
m/s

Answer 1

Answer 2

Given:

• Mass ($m$) = 14.0 kg

• Pulling force ($F_{\text{pull}}$) = 91.0 N

• Angle ($\theta$) = 18.0° above horizontal

• Duration ($t$) = 1.41 s

• Frictionless surface

• 
  

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(a) Forces Acting on the Block:

1. Pulling Force ($F_{\text{pull}}$):

• Horizontal component:

  $$F_{\text{pull, x}}=F_{\text{pull}}\cos \theta =91.0\cos 18.0\mathrm{°}=86.53\text{N}$$

• Vertical component:

  $$F_{\text{pull, y}}=F_{\text{pull}}\sin \theta =91.0\sin 18.0\mathrm{°}=28.12\text{N}$$

2. Gravitational Force ($F_g$):

   $$F_g=mg=14.0\times 9.81=137.34\text{N}$$

3. Normal Force ($F_N$):

• Balances $F_g$ and the vertical component of $F_{\text{pull}}$:

  $$F_N=F_g-F_{\text{pull, y}}=137.34-28.12=109.22\text{N}$$

Answers for (a):
| $F_{\text{pull}}$ | = | 91.0 N |
| $F_g$ | = | 137.34 N |
| $F_N$ | = | 109.22 N |

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(b) Final Speed of the Block:

1. Horizontal Acceleration ($a$):

   $$a=\frac{F_{\text{pull, x}}}{m}=\frac{86.53}{14.0}=6.18{\text{m/s}}^2$$

2. Final Speed ($v$):

   $$v=at=6.18\times 1.41=8.71\text{m/s}$$

Answer for (b):
The ice moves at 8.71 m/s after pulling.