A worker drags a crate across a factory floor by pulling on a rope tied to the crate.The worker exerts a force of magnitude F " 450 N on the rope,which is inclined at an upward angle u " 383 to the horizontal, and the floor exerts a horizontal force of magnitude f " 125 N that opposes the motion. Calculate the magnitude of the acceleration of the crate if (a) its mass is 310 kg and (b) its weight is 310 N.

Open in App

Solution

Although the full specification of ${\to F}_{n e t} = m \to a$ in this situation involves both x and y axes, only the x-application is needed to find what this particular problem asks for. We note that $a_{y} = 0$ so that there is no ambiguity denoting ax simply as a. We choose +x to the right and +y up. The free-body diagram (not to scale) is shown below.

The x component of the rope’s tension (acting on the crate) is

$F_{x} = F c o s θ = (450 N) c o s 38^{o} = 355 N$ ,

and the resistive force (pointing in the –x direction) has magnitude $f = 125 N$ .

(a) Newton’s second law leads to

$F_{x} - f = m a \Rightarrow a = \frac{F c o s θ - f}{m} = \frac{355 N - 125 N}{310 k g} = 0.74 m / s^{2}$ .

(b) In this case, we use Eq. 5-12 to find the mass: $m^{'} = W / g = 31.6 k g$ . Now, Newton’s second law leads to

$F_{x} - f = m^{'} a^{'} \Rightarrow a^{'} = \frac{F_{x} - f}{m^{'}} = \frac{355 N - 125 N}{31.6 k g} = 7.3 m / s^{2}$

Suggest Corrections

Similar questions

Q. A crate of weight

w

is dragged across the floor from

A

B

by a constant vertical force

F

acting at the end of the rope. Assuming that the crate does not lift off. The work done on the crate by the force

F

is:

A crate (box) rests on a smooth horizontal surface and a person pulls it with a $10 N$ force. Rank the situations shown below according to the magnitude of the normal force exerted by the surface on the crate, from the least to the greatest.

Q. Two crates of mass 75 kg and 110 kg, are in contact and rest on a horizontal surface. A 730 N force is exerted on 75Kg crate . If the coefficient of kinetic friction is 0.15 , calculate the acceleration of the system, and he force that each crate exerts on the other.

Q. A painter of mass

100 kg

is raising himself and the crate (such an arrangement is called Bosun's chair) on which he stands as shown. When he pulls the rope the force exerted by him on the crate's floor is

450 N

. If the crate weighs

25 kg

then, find the acceleration of the system and the tension in the rope.

Q. A worker is raising himself and the crate on which he stands with an acceleration of

5 {ms}^{- 2}

by a massless rope and pulley arrangement. Mass of the worker is

100 kg

and that of the crate is

50 kg

. If

T

is the tension in the rope and

F

be the force of contact between the worker and the floor and if

g = 10 {ms}^{- 2}

, then

Join BYJU'S Learning Program