Question

1. how much force is needed to accelerate a 60 kg skier at 2 m/sec²?
2. what is the force on a 1000 kg elevator that is falling freely at 9.8 m/sec²?
3. what is the acceleration of a 50 kg object pushed with a force of 200 n?
4. the mass of a large car is 1000 kg. how much force would be required to accelerate the car at a rate of 3 m/sec²?
5. a 50 kg skater pushed by a friend accelerates 5 m/sec². how much force did the friend apply?
6. a force of 250 n is applied to an object that accelerates at a rate of 5 m/sec². what is the mass of the object?
7. a bowling ball rolled with a force of 15 n accelerates at a rate of 3 m/sec²; a second ball rolled with the same force accelerates 4 m/sec². what are the masses of the two balls?
8. if a 60 kg person on a 15 kg sled is pushed with a force of 300 n, what will be person’s acceleration?
9. a force of 20 n acts upon a 5 kg block. calculate the acceleration of the object.
10. an object of mass 300 kg is observed to accelerate at the rate of 4 m/s². calculate the force required to produce this acceleration.
11. a 5 kg block is pulled across a table by a horizontal force of 40 n with a frictional force of 8 n opposing the motion. calculate the acceleration of the object.
12. an object of mass 30 kg is in free - fall in a vacuum where there is no air resistance. determine the acceleration of the object.
13. an object of mass 30 kg is falling in air and experiences a force due to air resistance of 50 newtons.

a. determine the net force acting on the object and
b. calculate the acceleration of the object.

Explanation:

Step1: Recall Newton's second - law

The formula is $F = ma$, where $F$ is force in Newtons (N), $m$ is mass in kilograms (kg), and $a$ is acceleration in meters per second squared ($m/s^{2}$). We will use this formula to solve each problem.

Problem 1:

Given $m = 60$ kg and $a= 2$ $m/s^{2}$, find $F$.
$F=ma=60\times2 = 120$ N

Problem 2:

Given $m = 1000$ kg and $a = 9.8$ $m/s^{2}$ (acceleration due to gravity for free - fall near Earth's surface), $F=ma=1000\times9.8=9800$ N

Problem 3:

Given $F = 500$ N and $m = 50$ kg, find $a$.
$a=\frac{F}{m}=\frac{500}{50}=10$ $m/s^{2}$

Problem 4:

Given $m = 1000$ kg and $a = 3$ $m/s^{2}$, $F=ma=1000\times3 = 3000$ N

Problem 5:

Given $m = 50$ kg and $a = 5$ $m/s^{2}$, $F=ma=50\times5=250$ N

Problem 6:

Given $F = 250$ N and $a = 5$ $m/s^{2}$, $m=\frac{F}{a}=\frac{250}{5}=50$ kg

Problem 7:

For the first ball: Given $F = 15$ N and $a = 3$ $m/s^{2}$, $m_1=\frac{F}{a}=\frac{15}{3}=5$ kg
For the second ball: Given $F = 15$ N and $a = 4$ $m/s^{2}$, $m_2=\frac{F}{a}=\frac{15}{4}=3.75$ kg

Problem 8:

The total mass $m=m_{person}+m_{sled}=60 + 15=75$ kg, and $F = 300$ N.
$a=\frac{F}{m}=\frac{300}{75}=4$ $m/s^{2}$

Problem 9:

Given $F = 20$ N and $m = 5$ kg, $a=\frac{F}{m}=\frac{20}{5}=4$ $m/s^{2}$

Problem 10:

Given $m = 300$ kg and $a = 4$ $m/s^{2}$, $F=ma=300\times4 = 1200$ N

Problem 11:

The net force $F_{net}=F - f$, where $F = 40$ N and $f = 8$ N, so $F_{net}=40 - 8=32$ N.
Given $m = 5$ kg, $a=\frac{F_{net}}{m}=\frac{32}{5}=6.4$ $m/s^{2}$

Problem 12:

In free - fall in a vacuum, the acceleration of an object is equal to the acceleration due to gravity, $a = 9.8$ $m/s^{2}$

Problem 13a:

The force due to gravity $F_g=mg$, where $m = 30$ kg and $g = 9.8$ N/kg, so $F_g=30\times9.8 = 294$ N.
The air resistance $F_{air}=50$ N.
The net force $F_{net}=F_g - F_{air}=294-50 = 244$ N

Problem 13b:

Given $m = 30$ kg and $F_{net}=244$ N, $a=\frac{F_{net}}{m}=\frac{244}{30}\approx8.13$ $m/s^{2}$

Answer:

1. 120 N
2. 9800 N
3. 10 $m/s^{2}$
4. 3000 N
5. 250 N
6. 50 kg
7. 5 kg, 3.75 kg
8. 4 $m/s^{2}$
9. 4 $m/s^{2}$
10. 1200 N
11. 6.4 $m/s^{2}$
12. 9.8 $m/s^{2}$

13a. 244 N
13b. 8.13 $m/s^{2}$