Forces & Kinematics Practice Problems

A crash test dummy equipped with a force sensor is used to measure the impact force on a passenger during a frontal collision. The 55.00-kg dummy is buckled up with a seat belt. The car, initially moving at a speed of 60.00 km/h, collides with a thick wall. The airbag is deployed, and brings the dummy to rest at a distance of 125.0 cm. Determine the magnitude of the impact force on the dummy from the airbag as measured by the force sensor.

An athlete performing physical exercise squats then jumps vertically up attaining a maximum height of approximately 68 cm. However, the athlete's body above the knees typically rises approximately 55 cm above the ground. For the sake of simplification in the calculations, while yielding a plausible result, we shall assume that the whole body rises 68 cm. What launch speed when leaving the ground enables her to attain a height of 68 cm?

An unidentified object is advancing toward a nuclear facility along the x-direction at a constant speed of 40 m/s 2 km above the ground level. A 15 kg missile producing a thrust of 425 N and oriented vertically upward is placed at ground level in the same x-y plane as the object. The missile is fired up and hits the object. At the instant of launching the missile, calculate the horizontal distance separating the missile and the object.

A basketball player runs at a constant speed of 4.0 m/s along the positive x-axis while holding a 0.625-kg ball. The player releases the ball by applying a vertical force of 8.0 N on the ball. The player's target is to enter the ball through the basket rim from below. The ball and the rim are in the same xy plane. The vertical distance separating the player's hand and the rim is 2.0 m. Determine the horizontal distance left of the rim where the athlete should release the ball to achieve his target.

A horizontal cable is pulling a 55 kg refrigerator across a smooth surface. The fridge's velocity is constant and equal to +2m/s. Determine the tension in the cable.

A 450 kg spaceship accelerates vertically upward on the surface of Mars. The amount of force produced by the spaceship engine is 2.5 × 10⁴ N. Ignore the effect of resistive forces. Calculate the spaceship's vertical acceleration. The gravitational acceleration on Mars is 3.72 m/s².

A charged sphere of mass 150 g initially at rest is accelerated by the mean of a vertical electric force of magnitude 6.5 N. When the sphere reaches a height (h) of 0.50 m the electric force becomes zero. Calculate the maximum distance reached by the sphere above the height h. Ignore air resistance.

A missile encounters four forces during a purely vertical flight: gravity, propulsion, and aerodynamic forces- lift and drag. Using the equations that model the launch of a missile, find an expression for the magnitude of missile velocity at an altitude 2h if aerodynamic forces are ignored.

A 1.25 kg box is being moved up an incline. The forces applied during the motion are shown in the figure below. Calculate the horizontal and vertical components of the box's acceleration vector.

A 6.0 kg box initially stationary at x = 0 m is subject to a horizontal variable force shown in the figure below. Calculate the acceleration of the box and its velocity after 5.0 s.

A professional football player kicks a 450 g ball at a speed of 90 km/h. The goalkeeper stops the ball with his hands and brings it to rest in 0.5 s. Calculate the strength of the force applied by the goalkeeper to stop the ball.

A thrill-seeker, Alex, decides to try bungee jumping off a bridge over a scenic river. The bungee cord he uses is highly elastic, designed to stretch and slow down the jumper safely. Alex jumps off the bridge and falls freely for a distance of 25.0 m before the bungee cord begins to stretch. The cord stretches an additional 15.0 m before momentarily stopping Alex. Calculate the average force exerted on Alex by the bungee cord during deceleration. Express your answer in multiples of Alex's weight, assuming the force exerted by the bungee cord is constant.

A 16-g pebble is thrown straight into a pile of sand at a speed of 370 m/s. After traveling 10 cm into the sand, the pebble stops. Calculate using kinematics and dynamics, the average force exerted by the sand onto the pebble.

A climber, Mike, decides to perform a controlled descent off a bridge using a static rope. The static rope, while having minimal elasticity, is designed to absorb some energy during falls or sudden loads. Mike steps off the bridge and is allowed to fall freely for a distance of 25.0 m before the static rope begins to slow his descent. The rope stretches 0.30 m to safely decelerate Mike to a stop. Calculate the average force exerted on Mike by the static rope during deceleration. Express your answer in multiples of Mike's weight, assuming the force exerted by the rope is constant.

As you near an intersection on your bicycle, which weighs 12 kg, traveling at a speed of 8.0 m/s, you find yourself 30 m from the intersection just as the traffic light switches to yellow. Anticipating that the yellow light will last for 5.0 s, and considering the intersection spans 20 m across, you decide to increase your pedaling effort to ensure a safe passage. Considering your mass of 60 kg and your ability to apply a forward force of 150 N through pedaling, can you successfully navigate the entirety of the intersection before the light turns red?

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A car traveling at a speed of 20 m/s approaches a red light and comes to a stop over a distance of 30 m along a flat road. If the mass of the car is 1000 kg, determine the average retarding force acting on the car to bring it to a stop.

A force of 800 N acting at an angle of 25° above the negative x-axis is applied to an 80 kg box that has wheels attached at its bottom. Determine the horizontal acceleration experienced by the box.

Hint: Assume the ground is frictionless.

A force of 150 N acting at an angle of 20° below the negative x-axis is applied to a stationary sled weighing 50 kg. If the force was exerted for 0.8 seconds to bring the sled in motion, determine the speed of the sled the moment the force is removed. Assume the ground is frictionless.

A car was initially at rest at the origin. It started to accelerate in a straight line as a result of a force acting on it, given by $F_{c}=Kt$. If the mass of the car is $m_{c}$, find as a function of time its velocity $v_{c}$ and position $x_{c}$.

A climber accidentally slips off a cliff and falls freely from a height of 20 m before landing in a snowbank that compresses 1.5 m to cushion the fall. If the climber has a mass of 60 kg, calculate the average decelerating force exerted by the snowbank during the climber's landing.

Consider a skydiver with a mass of 70.0 kg falling vertically from a plane. As the skydiver descends, they experience air resistance, which increases as their velocity increases. The drag force acting on the skydiver can be described by the equation F_D = −cv², where v is the velocity of the skydiver and c is the drag coefficient. Determine the terminal velocity of the skydiver.

A body is initially ascending vertically with velocity of 1.5 m/s at t = 0. Develop an equation characterizing its velocity over time, accounting for both gravity and a resistive force F = -cv.

A parachutist jumps from an airplane and experiences air resistance that can be modeled by the equation $a=\frac{d v}{d t}=g-c_{d} v$ , where $g$ is the acceleration due to gravity and $c_{d}$ is the drag coefficient related to the parachutist and their equipment. Determine an expression for the terminal velocity of the parachutist as a function of $g$ and $c_{d}$.

A weather balloon payload with a mass of 20 kg is released from a height of 500 m. As it falls back to Earth, it achieves a final velocity of 25 m/s due to air resistance. Determine the average force encountered by the payload during its descent. 

A 2 × 10^-5 kg pollen grain's terminal velocity is about 8 m/s. Given the drag force F_D = -bv, how long does it take to achieve 62% of this speed for a pollen grain starting from rest?