Math Problem Statement

We are having a physics test on forces and Universal Gravitation and the questions give is 2150 kg, 15.3m/s after 21 seconds , speed 9.17 m/s what is the average net force acting?

Solution

To determine the average net force acting on the object, we can use Newton's second law of motion, which is:

Favg=ΔpΔtF_{\text{avg}} = \frac{\Delta p}{\Delta t}

where:

  • FavgF_{\text{avg}} is the average net force,
  • Δp\Delta p is the change in momentum,
  • Δt\Delta t is the time interval.

Momentum pp is calculated as:

p=mvp = mv

where mm is the mass and vv is the velocity.

Step 1: Calculate the initial and final momentum.

Given:

  • Mass m=2150kgm = 2150 \, \text{kg},
  • Initial velocity v0=9.17m/sv_0 = 9.17 \, \text{m/s},
  • Final velocity vf=15.3m/sv_f = 15.3 \, \text{m/s}.

The change in momentum Δp\Delta p is:

Δp=m(vfv0)\Delta p = m(v_f - v_0)

Step 2: Calculate the average net force.

We are also given that the time interval Δt=21seconds\Delta t = 21 \, \text{seconds}.

Now, let's compute the average net force using the formula:

Favg=m(vfv0)ΔtF_{\text{avg}} = \frac{m(v_f - v_0)}{\Delta t}

Let me calculate this for you.

Given data mass = 2150 # kg v_0 = 9.17 # m/s (initial velocity) v_f = 15.3 # m/s (final velocity) delta_t = 21 # seconds

Calculate change in momentum

delta_p = mass * (v_f - v_0)

Calculate average net force

F_avg = delta_p / delta_t F_avgThe average net force acting on the object is approximately 627.6N627.6 \, \text{N} (Newtons).

Would you like further details on this calculation or have any questions?

Here are some related questions you could explore:

  1. How would the result change if the mass of the object was different?
  2. What is the relationship between velocity and force in the context of Newton's second law?
  3. How would you calculate the gravitational force between two objects using Universal Gravitation?
  4. What is the significance of the time interval in calculating average net force?
  5. How does the direction of the force affect the motion of the object?

Tip: When calculating net force from momentum, make sure to track the direction of velocity, as the force's direction depends on whether the velocity is increasing or decreasing.

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Math Problem Analysis

Mathematical Concepts

Newton's Second Law of Motion
Momentum
Force Calculation

Formulas

F_avg = Δp / Δt
p = mv

Theorems

Newton's Second Law
Conservation of Momentum

Suitable Grade Level

Grades 9-12