Which of the following statements is true regarding the direction of impulse and change in momentum?
The direction of impulse is always opposite to the direction of change in momentum
The direction of impulse is always perpendicular to the direction of change in momentum
The direction of impulse is always the same as the direction of change in momentum
The direction of impulse is independent of the direction of change in momentum
This question tests the understanding of the relationship between impulse and change in momentum, which is a fundamental concept in classical mechanics. The impulse-momentum theorem directly relates these two quantities.
C) The direction of impulse is always the same as the direction of change in momentum. This statement is correct because the impulse-momentum theorem (\(J = \Delta p\)) establishes a direct vector equality between impulse and change in momentum. For two vectors to be equal, they must have the same magnitude and the same direction.
What is the magnitude of the impulse experienced by a 60 kg skater who applies a constant force of 200 N to stop in 2 seconds?
The problem asks for the magnitude of the impulse experienced by a skater. Impulse is defined as the product of the force applied and the time duration over which the force acts. It can also be defined as the change in momentum. In this case, we are given the constant force and the time duration, so we can directly calculate the impulse using the force-time definition.
Impulse (\(J\)) is given by the product of the force (\(F\)) and the time interval (\(\Delta t\)) over which the force acts:
\[ J = F \times \Delta t \]The magnitude of the impulse experienced by the skater is \(400 \text{ N} \cdot \text{s}\).
Correct Option: B) 400 N·s
The question asks about the factors affecting the magnitude of impulse. We need to recall the definition and formula for impulse in physics.
A) Magnitude of force and duration of time
This option directly aligns with the definition and formula of impulse (\(J = F \times \Delta t\)). Both the force applied and the time duration of its application are crucial in determining the impulse experienced by an object.
This question asks about the relationship between mass, velocity, and momentum. We need to recall the formula for momentum and apply the given conditions (mass halved, velocity constant) to determine the change in momentum.
Recall the formula for momentum: Momentum (\(p\)) is defined as the product of an object's mass (\(m\)) and its velocity (\(v\)).
\[ p = m \times v \]Define the initial conditions: Let the initial mass of the object be \(m_1\) and its initial velocity be \(v_1\). The initial momentum (\(p_1\)) is then:
\[ p_1 = m_1 \times v_1 \]Define the new conditions: According to the problem, the mass of the object is halved, so the new mass (\(m_2\)) is \(m_1 / 2\). The velocity remains constant, so the new velocity (\(v_2\)) is equal to the initial velocity (\(v_1\)).
\[ m_2 = \frac{m_1}{2} \]\[ v_2 = v_1 \]Calculate the new momentum: Substitute the new mass and velocity into the momentum formula to find the new momentum (\(p_2\)):
\[ p_2 = m_2 \times v_2 \]\[ p_2 = \left(\frac{m_1}{2}\right) \times v_1 \]\[ p_2 = \frac{1}{2} \times (m_1 \times v_1) \]Compare the new momentum with the initial momentum: From step 2, we know that \(p_1 = m_1 \times v_1\). Substituting this into the equation from step 4:
\[ p_2 = \frac{1}{2} \times p_1 \]This shows that the new momentum is half of the initial momentum.
B) It is halved. As derived, when the mass is halved and velocity remains constant, the momentum becomes half of its original value.
To find the momentum of an object, we use the fundamental formula that defines momentum as the product of its mass and velocity. We are given the mass and velocity of the object, so we can directly apply this formula.
Momentum (\(p\)) is given by the product of mass (\(m\)) and velocity (\(v\)).
\[ p = m \times v \]The unit of momentum is kilogram-meter per second (kg m/s).
C) 90 kg m/s is the correct answer, as calculated by multiplying the mass (15 kg) by the velocity (6 m/s).
The question asks for the correct expression for impulse. Impulse is a fundamental concept in physics, particularly in mechanics, and is related to force and the duration over which the force acts. We need to recall the definition of impulse and its relationship with other physical quantities like force, time, momentum, mass, and acceleration.
Definition of Impulse: Impulse (\(J\)) is defined as the product of the average force (\(F\)) acting on an object and the time interval (\(\Delta t\)) for which the force acts.
Mathematically, this can be written as:
\[ J = F \times \Delta t \]
where \(J\) is impulse, \(F\) is the force, and \(\Delta t\) is the time interval.
Impulse-Momentum Theorem: Impulse is also equal to the change in momentum (\(\Delta p\)) of an object. Momentum (\(p\)) is the product of mass (\(m\)) and velocity (\(v\)), i.e., \(p = m \times v\).
\[ J = \Delta p = p_{\text{final}} - p_{\text{initial}} \]
Combining these definitions, we get:
\[ F \times \Delta t = \Delta p \]
Comparing the given options with the definition of impulse, we can identify the correct expression.
Correct Option: B) Impulse = Force × Time
This option directly matches the definition of impulse as the product of force and the time duration over which the force acts.