The coefficient of static friction is between the two blocks in FIGURE . The coefficient of kinetic friction between the lower block and the floor is . Forcecauses both blocks to cross a distance of , starting from rest. What is the least amount of time in which this motion can be completed without the top block sliding on the lower block?
The smallest amount amount of your time within which the motion will be completed is . .
The free body diagram of the upper block is provided within the below figure.
In the above figure, is that the force applied to the upper block, is that the mass of upper block, is that the burden of the upper block, is that the acceleration due to gravity, is that the traditional force on the upper block, and is that the force of static friction between the upper and lower bocks.
For upper block, the standard force balances its weight . So, the net force on the upper block along vertical direction is capable zero. Thus,Thus, the net force on the upper block along horizontal direction is,As the upper block remains on the lower block, the web force thereon is capable zero. So, the above equation is also rearranged as follows:
The static friction are often expressed in terms of coefficient of static friction and so the traditional force. So, the static friction force between the blocks is,
Similarly, the free body diagram of the lower block is shown within the below figure.
In the above figure is that the kinetic friction force between the lower block and thus the ground , is that the mass of the lower block, is that the traditional force on the lower block, and is that the total weight of lower and upper blocks.
For the lower block, the normal force balances the weight . Thus,The net force on the lower block along the horizontal direction is,The kinetic friction is expressed in terms of coefficient of kinetic friction and so the conventional force. So, the kinetic friction force between the lower block and floor is,Replace with .The net force of the lower block may additionally be expressed in terms of its mass and acceleration as follows:Here, is that the acceleration of the system.Replace with with and with in and rearrange the resulting equation for .
Substitute for for , for for and for
Thus, the acceleration of the system is
Round off to significant figures, the time taken for the system of blocks to cover the given distance is .
A car pushes a truck that has a dead battery. When the driver steps on the accelerator, the drive wheels of the car push against the ground with a force of . Rolling friction can be neglected.
a. What is the magnitude of the force of the car on the truck?
b. What is the magnitude of the force of the truck on the car?
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