5.3 Newton's second law  (Page 7/8)

A cleaner pushes a 4.50-kg laundry cart in such a way that the net external force on it is 60.0 N. Calculate the magnitude of his cart’s acceleration.

Astronauts in orbit are apparently weightless. This means that a clever method of measuring the mass of astronauts is needed to monitor their mass gains or losses, and adjust their diet. One way to do this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of 50.0 N is exerted, and an astronaut’s acceleration is measured to be $0.893{\text{m/s}}^2$ . (a) Calculate her mass. (b) By exerting a force on the astronaut, the vehicle in which she orbits experiences an equal and opposite force. Use this knowledge to find an equation for the acceleration of the system (astronaut and spaceship) that would be measured by a nearby observer. (c) Discuss how this would affect the measurement of the astronaut’s acceleration. Propose a method by which recoil of the vehicle is avoided.

In [link] , the net external force on the 24-kg mower is given as 51 N. If the force of friction opposing the motion is 24 N, what force F (in newtons) is the person exerting on the mower? Suppose the mower is moving at 1.5 m/s when the force F is removed. How far will the mower go before stopping?

The rocket sled shown below decelerates at a rate of $196{\text{m/s}}^2$ . What force is necessary to produce this deceleration? Assume that the rockets are off. The mass of the system is $2.10\times {10}^3$ kg.

If the rocket sled shown in the previous problem starts with only one rocket burning, what is the magnitude of this acceleration? Assume that the mass of the system is $2.10\times {10}^3$ kg, the thrust T is $2.40\times {10}^4\text{N},$ and the force of friction opposing the motion is 650.0 N. (b) Why is the acceleration not one-fourth of what it is with all rockets burning?

What is the deceleration of the rocket sled if it comes to rest in 1.10 s from a speed of 1000.0 km/h? (Such deceleration caused one test subject to black out and have temporary blindness.)

Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. The first child exerts a force of 75.0 N, the second exerts a force of 90.0 N, friction is 12.0 N, and the mass of the third child plus wagon is 23.0 kg. (a) What is the system of interest if the acceleration of the child in the wagon is to be calculated? (See the free-body diagram.) (b) Calculate the acceleration. (c) What would the acceleration be if friction were 15.0 N?

A powerful motorcycle can produce an acceleration of $3.50{\text{m/s}}^2$ while traveling at 90.0 km/h. At that speed, the forces resisting motion, including friction and air resistance, total 400.0 N. (Air resistance is analogous to air friction. It always opposes the motion of an object.) What is the magnitude of the force that motorcycle exerts backward on the ground to produce its acceleration if the mass of the motorcycle with rider is 245 kg?

A car with a mass of 1000.0 kg accelerates from 0 to 90.0 km/h in 10.0 s. (a) What is its acceleration? (b) What is the net force on the car?

The driver in the previous problem applies the brakes when the car is moving at 90.0 km/h, and the car comes to rest after traveling 40.0 m. What is the net force on the car during its deceleration?

An 80.0-kg passenger in an SUV traveling at $1.00\times {10}^3$ km/h is wearing a seat belt. The driver slams on the brakes and the SUV stops in 45.0 m. Find the force of the seat belt on the passenger.

A particle of mass 2.0 kg is acted on by a single force ${\overrightarrow{F}}_1=18\widehat{i}\text{N}.$ (a) What is the particle’s acceleration? (b) If the particle starts at rest, how far does it travel in the first 5.0 s?

Suppose that the particle of the previous problem also experiences forces ${\overrightarrow{F}}_2=\mathrm{-15}\widehat{i}\text{N}$ and ${\overrightarrow{F}}_3=6.0\widehat{j}\text{N}.$ What is its acceleration in this case?

Find the acceleration of the body of mass 5.0 kg shown below.

In the following figure, the horizontal surface on which this block slides is frictionless. If the two forces acting on it each have magnitude $F=30.0\text{N}$ and $M=10.0\text{kg}$ , what is the magnitude of the resulting acceleration of the block?