Question Video: Calculating the Pressure on an Angled Slab Due to the Weight of Object Physics • 9th Grade

A cube sits on a slab of wood which is mounted at an angle of 15 degrees to the horizontal, as shown in the figure. The cube weighs 40 N and has a side length of 5 cm. Calculate the pressure on the wooden slab due to the weight of the cube.

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Video Transcript

A cube sits on a slab of wood which is mounted at an angle of 15 degrees to the horizontal, as shown in the figure. The cube weighs 40 newtons and has a side length of five centimeters. Calculate the pressure on the wooden slab due to the weight of the cube.

In this question, we have a cube sitting on a slab of wood. And we want to calculate the pressure on the wooden slab due to the weight of the cube. We can recall that the pressure 𝑝 on an area 𝐴 is given by the equation 𝑝 equals 𝐹 over 𝐴, where 𝐹 is the force acting perpendicularly to the area.

We are told in the question that the cube weighs 40 newtons. This is the weight, which we will label as 𝑊, and this is a force that acts vertically downwards. However, to calculate the pressure on the wooden slab, we need the component of force that acts perpendicular to the face of the cube that is resting on the wooden slab.

So let’s resolve the weight into two independent components: one that acts parallel to the wooden slab, which we will label as 𝐹 sub 𝑥, and the other component that acts perpendicular to the slope, which we will label as 𝐹 sub 𝑦. We can now use the definition of cosine to find that cos 15 degrees equals 𝐹 sub 𝑦 over 𝑊. If we multiply both sides of this expression by 𝑊, then we find that the force 𝐹 sub 𝑦 is equal to 𝑊 multiplied by cos 15 degrees.

We now need to calculate the area of the face of the cube that is resting on the wooden slab. We are told in the question that the cube has a side length of five centimeters, which is equal to 0.05 meters. The face of the cube is a square. So the area 𝐴 will be equal to 0.05 meters multiplied by 0.05 meters, which is equal to 2.5 times 10 to the power of negative three meters squared.

Now that we have values for the force acting perpendicular to the wooden slab and the area of the face resting on the wooden slab, we can now calculate the pressure on the wooden slab. Substituting the values into our equation for pressure, we find that the pressure 𝑝 is equal to 40 newtons multiplied by cos 15 degrees over 2.5 times 10 to the power of negative three meters squared. Completing this calculation, we find that pressure is equal to 15455 newtons per meter squared to the nearest whole number. And this is our final answer.

The pressure on the wooden slab due to the weight of the cube is equal to 15455 newtons per meter squared.