# Forces

##### F=ma
1. How much force is necessary to push a 5.0kg box at 6 m/sÂČ?
2. What is the resulting acceleration if a 145g baseball is pushed with a 15.0 N force?
3. What is the mass of an object if when it undergoes a 35.0N force it accelerates at 7.0 m/sÂČ?
4. If a bowling ball accelerates at 3.5m/sÂČ and has a mass of 2.5kg what force is applied to it?
##### Force Diagrams
1. If two people try to lift a 400kg stone table off of the ground, one pulling straight up with a force of 1000N and the other pulling it at an angle of 60Âș from the ground with a force of 1200N will they be able to lift the table? Â What is the normal force of the floor on the table? Â What will be the acceleration of the table?
2. As you know monkeys swing between trees holding onto vines. Â If a monkey is holding one vine at an angle of 45Âș behind her and the other atÂ 45Âș in front of her and the vines balance her mass of 45kg, what is the force she must apply to each vine?
3. If a package of mass 75kg is on an surface tilted at 20Âș to the ground and it has a rope attached to it which pulls with a force of 400N directly up, what is the normal force on the package? Â What is the acceleration of the package?
4. You have a child of mass 30kg on a slide which makes an angle of 60Âș with respect to the ground. You are slightly below the child but want to hold them in place so you push up against the child at an angle of 30Âș compared to the ground. Â What force must you exert to keep the child in place?
5. When one repels down the side of a cliff or wall, one uses a rope to counter the force of gravity. If a rope makes an angle of 30Âș compared to a wall and completely supports one’s weight which is 85kg, what is the normal force exerted by the wall?
6. In track and field a runner often pushes off against a block that is at an angle to start the race. Â If the block is at an angle of 60Âș what force must an athlete push against it with so that they have zero acceleration in the y-direction? Â What will be there x-acceleration?
##### Friction and Centripetal Acceleration
1. Consider the table in the above example (#1), but now also include the friction force between the table and the floor. If the coefficient of static friction between the table and the floor is 0.6 what will the table accelerate? Â What will be the magnitude of the friction force?
2. If a car of mass 800kg is moving at constant velocity and the coefficient of kinetic friction between the tires and the road is 0.45 what must be the force applied by the car engine on the car?
3. If a car is on a curved road which if extended to a circle would have a radius of 50m and the coefficient of static friction between the car’s tires and the road is 0.6 what is the fastest speed the car can travel on the road with without slipping? Â How about if the road is banked at 15Âș to the ground?
4. If you are on a roller coaster which makes a loop 15m in radius and the maximum acceleration you feel while making that loop is 5g (5 times the acceleration of gravity on the Earth’s surface), how fast must the roller coaster be going?
5. You can attach a wooden ball to a string and swing it around your head. If the wooden ball’s mass is 0.5kg and the length of the rope is 1.5m and the ball’s speed is 1.3m/s what angle will the rope make with respect to the horizontal?
##### Universal Gravity
1. What is the gravitational force between 2 people who each have a mass of Â 50.0kg and are separated from one another by 0.50m?
2. What is the centripetal acceleration of the Earth (mass = $5.98 \times 10^{24}$kg) as it orbits the Sun (mass = $1.99 \times 10^{30}$Â kg, Earth-Sun distance is $1.5 \times 10^8$ km)? Â What force is required to keep the Earth on its orbit? And how does this compare to the gravitational force between the Sun and Earth?
3. What is the gravitational acceleration on the surface of the Moon (mass = $7.35 \times 10^{24}$ kg, radius = 1737 km)?
4. How much greater is the force between the Earth and Sun than the force between the Earth and Moon?
5. How fast must a satellite travel to stay in a circular orbit 3,000km above Â Earth’s surface?