Calculate the net force, acceleration, or mass in each situation:
a) A 72 kg rugby player accelerates at 1.6 m/s2
[forward].
b) A 2.3 kg model rocket accelerates 12 m/s2
[up].
c) A cannon exerts a force of 2.4 x 104 N [E] on a 5.0 kg shell.
d) (b) A hockey stick hits a 160 g puck forward with a force of 24 N.
e) A driver brakes and the car accelerates at 1.2 m/s2
[backwards]. The net force on the car is 1400 N
[backwards].
f) A woman throws a shot put with a net force of 33 N [forward] with an acceleration of 6.0 m/s2
[forward].
To calculate the missing values, we can use Newton's second law of motion:
a) Given the mass (m) of the rugby player as 72 kg and the acceleration (a) as 1.6 m/s^2, we can calculate the net force using the formula F = m * a.
F = 72 kg * 1.6 m/s^2 = 115.2 N [forward]
b) Given the mass (m) of the model rocket as 2.3 kg and the acceleration (a) as 12 m/s^2, we can calculate the net force using the same formula.
F = 2.3 kg * 12 m/s^2 = 27.6 N [up]
c) Given the force (F) exerted by the cannon as 2.4 x 10^4 N [E] and the mass (m) of the shell as 5.0 kg, we can calculate the acceleration using the formula a = F / m.
a = (2.4 x 10^4 N) / (5.0 kg) = 4.8 x 10^3 m/s^2 [E]
d) Given the force (F) with which the hockey stick hits the puck as 24 N and the mass (m) of the puck as 160 g (0.16 kg), we can calculate the acceleration using the same formula.
a = (24 N) / (0.16 kg) = 150 m/s^2 [forward]
e) Given the net force (F) on the car as 1400 N [backwards], we can calculate the mass (m) using the formula F = m * a, where a is the acceleration. Rearranging the formula, we get m = F / a.
m = 1400 N / 1.2 m/s^2 = 1167 kg
f) Given the net force (F) exerted by the woman as 33 N [forward] and the acceleration (a) as 6.0 m/s^2 [forward], we can calculate the mass (m) using the same formula.
m = 33 N / 6.0 m/s^2 = 5.5 kg
To calculate the net force, acceleration, or mass in each situation, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by the acceleration.
a) Given:
Mass (m) = 72 kg
Acceleration (a) = 1.6 m/s^2
To calculate the net force (F):
F = m * a
F = 72 kg * 1.6 m/s^2
F = 115.2 N [forward]
b) Given:
Mass (m) = 2.3 kg
Acceleration (a) = 12 m/s^2
To calculate the net force (F):
F = m * a
F = 2.3 kg * 12 m/s^2
F = 27.6 N [up]
c) Given:
Force (F) = 2.4 x 10^4 N [E]
Mass (m) = 5.0 kg
To calculate the acceleration (a):
F = m * a
2.4 x 10^4 N = 5.0 kg * a
a = (2.4 x 10^4 N) / 5.0 kg
a = 4800 m/s^2 [E]
d) Given:
Force (F) = 24 N
Mass (m) = 160 g = 0.16 kg
To calculate the acceleration (a):
F = m * a
24 N = 0.16 kg * a
a = (24 N) / 0.16 kg
a = 150 m/s^2
e) Given:
Net force (F) = 1400 N [backwards]
Acceleration (a) = 1.2 m/s^2 [backwards]
To calculate the mass (m):
F = m * a
1400 N = m * 1.2 m/s^2
m = (1400 N) / 1.2 m/s^2
m = 1167 kg
f) Given:
Net force (F) = 33 N [forward]
Acceleration (a) = 6.0 m/s^2 [forward]
To calculate the mass (m):
F = m * a
33 N = m * 6.0 m/s^2
m = (33 N) / 6.0 m/s^2
m = 5.5 kg
To calculate the net force, acceleration, or mass in each situation, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. The formula can be represented as:
Net Force (F) = Mass (m) * Acceleration (a)
Let's calculate the values:
a) To calculate the net force, we are given the mass (m) of the rugby player as 72 kg and the acceleration (a) as 1.6 m/s². Using the formula, we can calculate the net force:
F = m * a
F = 72 kg * 1.6 m/s²
F = 115.2 N
Therefore, the net force acting on the rugby player is 115.2 N [forward].
b) We are given the mass (m) of the model rocket as 2.3 kg and the acceleration (a) as 12 m/s². Using the formula, we can calculate the net force:
F = m * a
F = 2.3 kg * 12 m/s²
F = 27.6 N
Therefore, the net force acting on the model rocket is 27.6 N [up].
c) We are given the force (F) exerted by the cannon as 2.4 x 10^4 N [E] and the mass (m) of the shell as 5.0 kg. Rearranging the formula, we can find the acceleration (a):
a = F / m
a = (2.4 x 10^4 N) / 5.0 kg
a = 4800 m/s²
Therefore, the acceleration of the shell is 4800 m/s².
d) We are given the force (F) exerted by the hockey stick as 24 N and the mass (m) of the puck as 160 g. Since the mass is given in grams, we need to convert it to kilograms:
mass (m) = 160 g / 1000 (to convert grams to kilograms)
m = 0.16 kg
Using the formula F = m * a, we can rearrange it to find the acceleration (a):
a = F / m
a = 24 N / 0.16 kg
a = 150 m/s²
Therefore, the acceleration of the puck is 150 m/s².
e) We are given the net force (F) on the car as 1400 N [backwards] and the acceleration (a) of the car as 1.2 m/s² [backwards]. Since the net force and acceleration have opposite directions, we need to give them opposite signs:
F = -1400 N
a = -1.2 m/s²
Using the formula F = m * a, we can rearrange it to find the mass (m):
m = F / a
m = -1400 N / -1.2 m/s²
m ≈ 1166.67 kg
Therefore, the mass of the car is approximately 1166.67 kg.
f) We are given the net force (F) exerted by the woman as 33 N [forward] and the acceleration (a) of the shot put as 6.0 m/s² [forward]. Using the formula F = m * a, we can rearrange it to find the mass (m):
m = F / a
m = 33 N / 6.0 m/s²
m ≈ 5.5 kg
Therefore, the mass of the shot put is approximately 5.5 kg.