1) An 8.5kg bowling ball dropped 11m hits the ground 1.5 seconds later. What is the magnitude of the force acting on the ball during the fall?
2) Shuttle astronauts climb at a rate of 24.5m/s^2 shortly after takeoff. What apparent weight would a 95kg astronaut have during this phase of the ascent?
3) A golf cart with driver has a mass of 320kg and accelerates at 1.4m/s^2. Assuming the force does not change, what would be the acceleration if a 70kg passenger gets on board?
1) The weight force, M*g
Note: The problem asks DURING the fall
2) (M + a)*g
3) F = 320*3.2 = (320 + 70)*a'
Solve for a'
1) To determine the magnitude of the force acting on the ball during the fall, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration. In this case, the acceleration experienced by the ball is due to gravity and can be calculated using the equation:
acceleration = gravitational field strength * time
The gravitational field strength on Earth is approximately 9.8 m/s^2.
So, the acceleration of the ball is:
acceleration = 9.8 m/s^2 * 1.5 s = 14.7 m/s^2
Next, we can use the equation:
force = mass * acceleration
Substituting the given values:
force = 8.5 kg * 14.7 m/s^2
Calculating the force gives us:
force = 125.95 N
Therefore, the magnitude of the force acting on the ball during the fall is 125.95 Newtons.
2) To find the apparent weight of the astronaut, we can use the equation:
apparent weight = mass * acceleration
Given that the acceleration during this phase of the ascent is 24.5 m/s^2 and the mass of the astronaut is 95 kg, we can substitute the values into the equation:
apparent weight = 95 kg * 24.5 m/s^2
Calculating the apparent weight yields:
apparent weight = 2327.5 N
Therefore, the apparent weight of the astronaut during this phase of the ascent is 2327.5 Newtons.
3) To determine the new acceleration of the golf cart with a passenger on board, we need to consider the additional mass of the passenger. According to Newton's second law, the acceleration depends on the net force acting on the object.
We can calculate the net force using the equation:
net force = mass * acceleration
Initially, the net force is given by:
net force = (mass of the golf cart + mass of the driver) * acceleration
Once the passenger gets on board, the net force becomes:
net force = (mass of the golf cart + mass of the driver + mass of the passenger) * new acceleration
Since the net force remains the same, we can set up the equation:
(mass of the golf cart + mass of the driver) * acceleration = (mass of the golf cart + mass of the driver + mass of the passenger) * new acceleration
Substituting the given values:
(320 kg + 70 kg) * 1.4 m/s^2 = (320 kg + 70 kg + 70 kg) * new acceleration
Simplifying the equation gives us:
390 kg * 1.4 m/s^2 = 460 kg * new acceleration
Now, solving for the new acceleration:
new acceleration = (390 kg * 1.4 m/s^2) / (460 kg)
Calculating the new acceleration yields:
new acceleration ≈ 1.185 m/s^2
Therefore, the acceleration of the golf cart with the passenger on board would be approximately 1.185 m/s^2.