A worker pushes horizontally on a crate with a force of magnitude . The coefficient of static friction between the crate and the floor is . (a) What is the value of under the circumstances? (b) Does the crate move? (c) What is the frictional force on the crate from the floor? (d) Suppose, next, that a second worker pulls directly upward on the crate to help out. What is the least vertical pull that will allow the first worker’s push to move the crate? (e) If, instead, the second worker pulls horizontally to help out, what is the least pull that will get the crate moving?
(a) The value of under the circumstances is 127 N.
(b) The crate does not move.
(c) The frictional force on the crate from the floor is 110 N.
(D) The least vertical pull that will allow the first worker’s push to move the crate is 47 N.
(E) The least magnitude of F’ to move the box should be 17N.
Coefficient of static friction,
External force on the crate,
The problem is based on Newton’s second law of motion which states that the rate of change of momentum of a body is equal in both magnitude and direction of the force acting on it. Use the Newton's 2nd law of motion along vertical and horizontal direction. According to Newton's 2nd law of motion, a force applied to an object at rest causes it to accelerate in the direction of the force.
where, F is the net force, m is mass and a is an acceleration.
Free body Diagram of Crate:
By using Newton’s 2nd law along vertical direction (along y),
Since crate is not moving upward,
Relation between maximumstatic frictional force and normal force is,
Hence, the value of under the circumstances is 127 N.
Hence, the crate does not move.
By using Newton’s 2nd law along the horizontal direction,
Since crate is not moving,
Hence, the frictional force on the crate from the floor is .
Let, the upward force apply by the worker is F’, then by using Newton’s 2nd law,
since crate is not moving upward,
In order to move the crate F must satisfy the condition,
Since,F’ is slightly greater than .
Hence, the least vertical pull that will allow the first worker’s push to move the crate is 47 N.
If the horizontal force applied by the worker is F’ and to move the box the total forward force should overcome the backward static frictional force
Therefore, the least magnitude of F’ to move the box should be .
In Fig. 6-61 a fastidious worker pushes directly along the handle of a mop with a force. The handle is at an anglewith the vertical, andandare the coefficients of static and kinetic friction between the head of the mop and the floor. Ignore the mass of the handle and assume that all the mop’s mass m is in its head. (a) If the mop head moves along the floor with a constant velocity, then what is F? (b) Show that if. is less than a certain value, then(still directed along the handle) is unable to move the mop head. Find.
Figure 6-53 shows a conical pendulum, in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass of 0.040 kg , the string has length L=0.90 m and negligible mass, and the bob follows a circular path of circumference 0.94 m . What are
(a) the tension in the string and
(b) the period of the motion?
During a routine flight in 1956, test pilot Tom Attridge put his jet fighter into adive for a test of the aircraft’s 20 mm machine cannons. While traveling faster than sound at 4000 m altitude, he shot a burst of rounds. Then, after allowing the cannons to cool, he shot another burst at 2000 m ; his speed was then 344 m/s, the speed of the rounds relative to him was 730 m/s, and he was still in a dive. Almost immediately the canopy around him was shredded and his right air intake was damaged. With little flying capability left, the jet crashed into a wooded area, but Attridge managed to escape the resulting explosion. Explain what apparently happened just after the second burst of cannon rounds. (Attridge has been the only pilot who has managed to shoot himself down.)
The floor of a railroad flatcar is loaded with loose crates having a coefficient of static friction 0.25 of with the floor. If the train is initially moving at a speed of 48 km/h, in how short a distance can the train be stopped at constant acceleration without causing the crates to slide over the floor?
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