Gravitational Force Through Real-World Examples

A 2.0 kg book is lying on a 0.75-m-high table. You pick it up and place it on a bookshelf 2.3 m above the floor. During this process, 
How much work does gravity do on the book?

The rope and pulley have negligible mass, and the pulley is frictionless. The coefficient of kinetic friction between the 
8.00-kg block and the tabletop is ${\displaystyle \mu k=0.250}$. The blocks are released from rest. Use energy methods to calculate the speed of the 6.00-kg block after it has descended 1.50 m. 

3.19 Win the Prize. In a carnival booth, you can win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of 2.1 m from this point (Fig. E3.19). If you toss the coin with a velocity of 6.4 m/s at an angle of 60° above the horizontal, the coin will land in the dish. Ignore air resistance. (a) What is the height of the shelf above the point where the quar ter leaves your hand? (b) What is the vertical component of the velocity of the quarter just before it lands in the dish?

From her bedroom window a girl drops a water-filled balloon to the ground 6.0 m below. If the balloon is released from rest,how long is it in the air?

A block of mass m=2.20 kg slides down a 30 degree incline which is 3.60 m high. At the bottom, it strikes a block of mass=7.00 kg which is at rest on a horizontal surface in the picture. If the collision is elastic, and friction can be ignored, determine (a)the speeds of the two blocks after the collision, and (b) how far back up the incline the smaller mass will go.

A model airplane of mass 0.750 kg flies in a horizontal circle at the end of a 60.0 m control wire, with a speed of 35.0 m/s. Compute the tension in the wire if it makes a constant angle of 20.0° with the horizontal. The forces exerted on the airplane are the pull of the control wire, the gravitational force, and aerodynamic lift, which acts at 20.0° inward from the vertical.

A 5.00 kg package slides 1.50 m down a long ramp that is inclined at ${\displaystyle {12.0}^{\circ }}$ below the horizontal. The coefficient of kinetic friction between the package and the ramp is k =0.310. Calculate 
(a) the work done on the package by friction (b) the workdone on the package by gravity (c) the work done on the package bythe normal force (d) the total work done on the package (e) Ifthe package has a speed of 2.20 m/s at the top of the ramp, what isits speed after sliding 1.50 m down the ramp?

A 15.0 kg block is dragged over a rough, horizontal surface by a70.0 N force acting at 20.0 degree angle above the horizontal. The block is displaced 5.0 m, and the coefficient of kinetic friction is 0.3. Find the work done on the block by ; a) the 70.0 N force,b) the normal force, and c) the gravitational force. d) what is the increase in the internal energy of the block-surface system due to friction? e) find the total change in the kinetic energy of the block.

An adventurous archaeologist crosses between two rock cliffs by slowly going hand-over-hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope (Fig. 1) The rope will break if the tension in it exceeds $4.50\cdot {10}^4$N and our hero's mass is 86.5 kg.

 Figure 1 a) If the angle $\theta$ is ${13.0}^{\circ }$, find the tension iin the rope.

b) What is the smallest value the angle $\theta$ can have if the rope is not to break?

A uniform plank of length 2.00 m and mass 30.0 kg is supported by three ropes. Find the tension in each rope when a 700-N person is 0.500 m from the left end.

A 0.450 kg ice puck, moving east with a speed of ${\displaystyle 3.00\frac{m}{s}}$ has a head in collision with a 0.900 kg puck, initially at rest. Assuming a perfectly elastic collision what will be the speed and direction of each object after the collision?

The specific gravity of ice is 0.917, whereas that for seawater is 1.025. What fraction of an iceberg is above the surface of the water?

A small rock with mass 0.12 kg is fastened to a massless string with length 0.80 m to form a pendulum. The pendulum is swinging so as to make a maximum angle of 45 with the vertical. Air Resistance is negligible. 
a) What is the speed of the rock when the string passesthrough the vertical position? 
b) What is the tension in the string when it makes an angle of 45 with the vertical? 
c) What is the tension in the string as it passes through the vertical? 
 

A block is on a frictionless table, on earth. The block accelerates at ${\displaystyle 5.3\frac{m}{s^2}}$ when a 10 N horizontal force is applied to it. The block and table are set up on the moon. The acceleration due to gravity at the surface of the moon is ${\displaystyle 1.62\frac{m}{s^2}}$. A horizontal force of 5N is applied to the block when it is on the moon. The acceleration imparted to the block is closest to: 
a) ${\displaystyle 2.9\frac{m}{s^2}}$ 
b) ${\displaystyle 3.2\frac{m}{s^2}}$ 
c) ${\displaystyle 3.4\frac{m}{s^2}}$ 
d) ${\displaystyle 2.7\frac{m}{s^2}}$ 
e) ${\displaystyle 2.4\frac{m}{s^2}}$

A 730-N man stands in the middle of a frozen pond of radius 5.0 m. He is unable to get to the other side because of a lack of friction between his shoes and the ice. To overcome this difficulty, he throws his 1.2 kg physics textbook horizontally toward the north shore , at a speed of 5.0 m/s. How long does ittake him to reach the south shore?

A space traveler weights 540 N on earth. what will the traveler weigh on another planet whose radius is three times that of earth and whose mass is twice that of earth ?

An Alaskan rescue plane drops a package of emergency rations to a stranded party of explorers. the plane is traveling horizontally at $30.0m/s$ at a height of $200.0m$ above the ground.

A)What horizontal distance does the package fall before landing?

B)Find the velocity of the package just before it hits the ground.

A ski tow operates on a 15.0 degrees slope of lenth 300m. The rope moves at 12.0km/h and provides power for 50 riders at one time, with an average mass per rider of 70.0kg. Estimate the power required to operate the tow.

The drawing shows a version of the loop-the-loop trick for a small car. If the car is given an initial speed of 4 m/s, what is the largest value that the radius r can have if the car is to remain in contact with the circular track at all times?

Raindrops make an angle theta with the vertical when viewed through a moving train window. If the speed of the train is v (subscript t), what is the speed of the raindrops in the reference frame of the Earth in which they are assumed to fall vertically?