Q: A construction crane lifts a steel girder of mass $$800\ \mathrm{kg} at an $$acceleration of $$0.20g. $$What is the tension in the lifting cable?

$$8.0 \times 10^3$\ \mathrm{N}$$

Q: A container of mass $$4520\ \mathrm{kg} is $$held by a slanted cable at $$58.0^\circ$$ from the vertical and a horizontal cable. What are the tensions $$T_1 ($$slanted) and $$T_2 ($$horizontal)?

$$T_1 = 4.43$$ \times $$10^4$$\ \mathrm{N};\ $$T_2 = 2.35$$ \times $$10^4$$\ \mathrm{N}$$

Question 1

A box is placed on a frictionless surface at the back of a pick-up truck. The truck suddenly accelerates forward. What happens to the box?

Accepted Answer

The box does not accelerate but will remain at constant velocity (at rest) until it hits the back of the pick-up.

Question 2

An 8.50 kg trolley is accelerating in a straight line in the x-axis direction. The acceleration of the trolley as a function of time is shown in the graph. At which time interval does the trolley experience a constant net force?

Accepted Answer

$$t = 7.0 - 12.0 \ \mathrm{ms}$$

Question 3

A 2.0-kg block is initially at rest and subjected to two forces for 3.0 s: $$\vec{F}_1 = (17\vec{i} + 13\vec{j})\ \mathrm{N}$$ and $$\vec{F}_2 = (11\vec{i} + 23\vec{j})\ \mathrm{N}. $$What is the velocity of the block at $$t = 3.0\ \mathrm{s}$$?

Accepted Answer

$$(9\vec{i} + 54\vec{j})\ \mathrm{m/s}$$

Question 4

A 55.0-kg crash test dummy is brought to rest from 60.00 km/h by an airbag over a distance of 1.25 m. What is the magnitude of the impact force measured by the force sensor?

Accepted Answer

$$6111\ \mathrm{N}$$

Question 5

A 16-g pebble is thrown into a pile of sand at $$370\ \mathrm{m/s}$$ and stops after traveling $$0.10\ \mathrm{m}. $$What is the average force exerted by the sand on the pebble?

Accepted Answer

$$11000\ \mathrm{N}$$

Question 6

A skydiver with mass $$70.0\ \mathrm{kg}$$ falls vertically and experiences air resistance described by $$F_D = -cv^2$. What is the terminal velocity v_t$ of the skydiver?

Accepted Answer

$$\dfrac{26.2}{\sqrt{c}}$$

Question 7

Three boats of masses 30 kg, 20 kg, and 10 kg are pulled along a frictionless surface by a rope with a total force of $$480\ \mathrm{N}. $$What are the tensions $$T_A$$ and $$T_B in $$the ropes between the boats?

Accepted Answer

$$T_A = 360.0\ \mathrm{N},\ T_B = 260.0\ \mathrm{N}$$

Question 8

A person draws a bucket of water from a well. The bucket accelerates upward at $$4.00\ \mathrm{m/s^2$}$$ and the tension in the rope is $$20.0\ \mathrm{N}. $$What is the mass of the bucket?

Accepted Answer

$$2.45\ \mathrm{kg}$$

Question 9

A construction crane lifts a steel girder of mass $$800\ \mathrm{kg} at an $$acceleration of $$0.20g. $$What is the tension in the lifting cable?

Accepted Answer

$$8.0 	imes 10^3$\ \mathrm{N}$$

Question 10

A $$145\ \mathrm{kg}$$ box slides at constant velocity down a frictionless incline at $$22.0^\circ$$ above the horizontal. If you push the box with a force parallel to the horizontal, what is the magnitude of the force?

Accepted Answer

$$1533\ \mathrm{N}$$

Question 11

Two trucks pull a storage container north with forces $$\vec{F}_1$$ and $$\vec{F}_2$$. $$\vec{F}_1 = 4400\ \mathrm{N} at$$ $$46^\circ$$ and $$\vec{F}_2 at$$ $$30^\circ. If $$the total force north is $$8538\ \mathrm{N}$$, what is the magnitude of $$\vec{F}_2$$?

Accepted Answer

$$\vec{F}_2$$ exerts $$6330\ \mathrm{N}$$, magnitude of total force $$8538\ \mathrm{N}$$

Question 12

A container of mass $$4520\ \mathrm{kg} is $$held by a slanted cable at $$58.0^\circ$$ from the vertical and a horizontal cable. What are the tensions $$T_1 ($$slanted) and $$T_2 ($$horizontal)?

Accepted Answer

$$T_1 = 4.43$$ 	imes $$10^4$$\ \mathrm{N};\ $$T_2 = 2.35$$ 	imes $$10^4$$\ \mathrm{N}$$

Question 13

A $$10\ \mathrm{kg}$$ box is pulled across a frictionless floor by a $$40\ \mathrm{N}$$ force at $$20^\circ$$ above the horizontal. What is the vertical component of the force?

Accepted Answer

$$13.7\ \mathrm{N}$$

Question 14

A $$5.0\ \mathrm{kg}$$ object is dropped from rest and falls $$20\ \mathrm{m}$$ before hitting the ground. Neglecting air resistance, what is its velocity just before impact?

Accepted Answer

$$19.8\ \mathrm{m/s}$$

Question 15

A $$2.0\ \mathrm{kg}$$ block is pushed across a rough surface with a force of $$10\ \mathrm{N}$$, and the coefficient of kinetic friction is $$0.3. $$What is the acceleration of the block?

Accepted Answer

$$2.15\ \mathrm{m/s^2$}$$

Question 16

A $$0.5\ \mathrm{kg}$$ ball is thrown vertically upward with an initial velocity of $$10\ \mathrm{m/s}. $$What is the maximum height reached?

Accepted Answer

$$5.1\ \mathrm{m}$$

Question 17

A $$3.0\ \mathrm{kg}$$ block is attached to a spring with spring constant $$k = 200\ \mathrm{N/m}$$ and pulled $$0.15\ \mathrm{m}$$ from equilibrium. What is the force exerted by the spring?

Accepted Answer

$$30\ \mathrm{N}$$

Question 18

A $$1.0\ \mathrm{kg}$$ object moves in a circle of radius $$2.0\ \mathrm{m} at$$ $$4.0\ \mathrm{m/s}. $$What is the centripetal force?

Accepted Answer

$$8.0\ \mathrm{N}$$

Dynamics and Forces: Study Guide with Applications

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