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Chapter 4: Problem 10

A dockworker applies a constant horizontal force of 80.0 N to a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves 11.0 m in 5.00 s. (a) What is the mass of the block of ice? (b) If the worker stops pushing at the end of 5.00 s, how far does the block move in the next 5.00 s?

Short Answer

Expert verified
(a) Mass of block = 90.91 kg. (b) Distance moved in next 5 s = 22.0 m.

Step by step solution

01

Determine Acceleration

Start by using the formula for constant acceleration: \[ a = \frac{2d}{t^2} \] where \( d = 11.0 \) m (distance) and \( t = 5.00 \) s (time). Plug in the values: \[ a = \frac{2 \times 11.0}{5.00^2} = \frac{22}{25} = 0.88 \text{ m/s}^2 \].
02

Use Newton's Second Law to Find Mass

Using Newton's second law, \( F = ma \), where \( F = 80.0 \) N and \( a = 0.88 \text{ m/s}^2 \). Solve for \( m \): \[ m = \frac{F}{a} = \frac{80.0}{0.88} \approx 90.91 \text{ kg} \].
03

Determine Velocity at the End of 5 Seconds

Use \( v = u + at \) where \( u = 0 \text{ m/s} \), \( a = 0.88 \text{ m/s}^2 \), and \( t = 5.00 \text{ s} \): \[ v = 0 + (0.88)(5.00) = 4.4 \text{ m/s} \].
04

Calculate Additional Distance Moved

After the force stops, the block will move with constant velocity. Use \( s = vt \) for the next 5 seconds where \( v = 4.4 \text{ m/s} \) and \( t = 5.00 \text{ s} \): \[ s = (4.4)(5.00) = 22.0 \text{ m} \].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

constant acceleration
When an object moves with a constant acceleration, it accelerates at the same rate over time. This means that for every second that passes, the speed of the object increases by a consistent amount. This is a key concept in understanding the motion of objects where forces are applied. In this exercise, the acceleration is calculated using the formula for constant acceleration: \[ a = \frac{2d}{t^2} \]This formula helps determine how quickly an object speeds up as a result of a known force. In our example, the bloc of ice accelerates at a steady rate due to the constant force applied by the dockworker. Constant acceleration is essential in physics, as it lays the foundation for more advanced analyses of motion and is an integral part of many physics problems and real-world applications.Key Points:
  • Acceleration remains consistent over time
  • Useful for predicting future velocity and displacement
  • Relies on formulas relating distance, speed, and time
frictionless motion
Frictionless motion refers to a scenario where the moving object encounters no resistance from surfaces or the environment around it. In real-world terms, this means an object will continue to move smoothly as long as no additional forces act upon it. The exercise specifies that the ice block is on a smooth floor, indicating that we can ignore any frictional forces. This simplifies calculations significantly since friction usually acts to slow down motion. In frictionless motion, Newton's Second Law is especially useful as it allows us to calculate the mass and acceleration with fewer variables. Here, with no friction, the only force the dockworker needs to consider is the one applied directly to the ice block, making it an ideal condition to observe how an object behaves under pure acceleration without external resistance. Remember:
  • Motion is simplified without friction
  • Object moves smoothly without losing speed
  • Calculations involve only applied forces
basic kinematics
Basic kinematics involves the study of motion without considering the forces that cause it. In this exercise, basic kinematics is applied in calculating how far and fast the ice block moves. It provides the mathematical equations necessary to describe motion based on time, velocity, and displacement. One important kinematic equation used here is:\[ s = vt \]which calculates the distance moved after the force stops being applied, assuming the block continues at constant velocity. Kinematics focuses on motion descriptions using simple mathematical relations, guiding you from initial conditions like the block starting from rest to reaching a velocity of 4.4 m/s.Understanding kinematics means you can predict how long it will take an object to cover a certain distance or how fast it will be moving after a specific time鈥攙ital tools in problem-solving across various physics scenarios.Summary:
  • Describes motion using mathematical equations
  • Does not consider forces but focuses on the motion itself
  • Includes relations between velocity, distance, and time

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Most popular questions from this chapter

A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a horizontal force with magnitude 48.0 N to the box and produces an acceleration of magnitude 2.20 m/s\(^2\), what is the mass of the box?

A chair of mass 12.0 kg is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force \(F =\) 40.0 N that is directed at an angle of 37.0\(^\circ\) below the horizontal, and the chair slides along the floor. (a) Draw a clearly labeled free-body diagram for the chair. (b) Use your diagram and Newton's laws to calculate the normal force that the floor exerts on the chair.

A small 8.00-kg rocket burns fuel that exerts a timevarying upward force on the rocket (assume constant mass) as the rocket moves upward from the launch pad. This force obeys the equation \(F = A + Bt^2\). Measurements show that at \(t\) = 0, the force is 100.0 N, and at the end of the first 2.00 s, it is 150.0 N. (a) Find the constants \(A\) and \(B\), including their SI units. (b) Find the \(net\) force on this rocket and its acceleration (i) the instant after the fuel ignites and (ii) 3.00 s after the fuel ignites. (c) Suppose that you were using this rocket in outer space, far from all gravity. What would its acceleration be 3.00 s after fuel ignition?

The upward normal force exerted by the floor is 620 N on an elevator passenger who weighs 650 N. What are the reaction forces to these two forces? Is the passenger accelerating? If so, what are the magnitude and direction of the acceleration?

After an annual checkup, you leave your physician's office, where you weighed 683 N. You then get into an elevator that, conveniently, has a scale. Find the magnitude and direction of the elevator's acceleration if the scale reads (a) 725 N and (b) 595 N.
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